2.The
visual representation shown here helps describe the
relationship between mathematics placement-test scores
and writing-test scores for an incoming class of
students. The plot provides information about the _?_ of
that relationship.

A faculty group
seeks to determine whether job rating (call it x) is a
useful linear predictor of annual salary raise (call it y).
The group uses least-squares linear regression to determine this
prediction equation:

y =
-1782.83x + 14012.17.

5. Which one of the
following statements is most correct?

a. The
prediction equation assures that the actual raises for the 15
administrators fall in a perfect straight line.

b. The
prediction equation suggests that if we know an administrator's
job rating, we can determine his or her exact salary
raise.

c. The
prediction equation suggests that for the mean job rating an
administrator would get the mean salary increase.

d. The
prediction equation suggests that, on the average,
administrators have a poor job rating.

e. None of the
statements (a) through (d) are correct.

f. More than one
of the statements (a) through (d) are correct.

6. Which one of the
following statements about the prediction line y = -1782.83x +
14012.17 is least correct?

a. The equation
can be used to state the actual raise for an administrator by
knowing his or her job rating.

b. The equation
produces predicted raises with the sum of the squared residuals
minimized.

c. If the linear
model is accepted as valid, the equation could be used to
predict an administrator raise from an administrator's job
rating.

d. The equation
produces predicted raises with an average residual (average
error) of 0.

7. Which statement
best interprets the meaning of the slope of the prediction
equation?

a. For a 1-point
increase in an administrator job rating, we can estimate a
salary increase of $1782.83.

b. For a 1-point
increase in an administrator job rating, we can estimate a
salary decrease of $1782.83.

c. For an
administrator with a job rating of 1.00, we can estimate his or
her raise to be $1782.83.

d. For a $1
salary raise, we can estimate that the administrator job rating
will decrease by 1782.83.

8. True or
false: The best model to represent any two-variable data
set is a least-squares linear regression equation.

a.
True

b.
False

9 . A median-median
line is to be generated on a scatter plot. The plot has been
divided into three sections and a median-median point for each of
the three sections has been determined. What is the next step in
creating the median-median line?

a. Calculate the
slope of the median-median line.

b. Determine the
value of r, the correlation coefficient.

c. Draw an
ellipse around the points of the scatter plot.

d. Identify the
centroid of the data.

e. None of the
statements (a) through (d) correctly identify the next
step.

f. More than one
of the steps in statements (a) through (d) could be completed
next.

The following
situation is used for problems 10 through 14.

Emotional
exhaustion, or burnout, can be a significant
problem for college students. Researchers have used
linear models to investigate how emotional exhaustion may
relate to aspects of college life.

One study
considered how an index of exhaustion (determined through
responses to a questionnaire) related to what portion of
a person's social contact was with students in the same
program or field of study. The researchers called this
factor "concentration of contacts." The table here lists
the values of the emotional exhaustion index (higher
values indicate greater emotional exhaustion) and percent
concentration of contacts for a sample of 25 education
students from a large university.

It can be
shown that the equation for the median median line that
models this data set is y = 11.51x - 148.833.
Also, the equation of the least-squares linear regression
line for this data is y = 8.865x - 29.497, where
the sum of the squared residuals is 698,009.

10. True or
false: The slope of the least-squares regression line is
greater than the slope of the median-median line.

a.
True.

b.
False.

c. It cannot be
determined from the information provided.

11. The
median-median line model predicts that someone with a
concentration of 50% will have an emotional exhaustion index of
_?_.

a.
0.7825

b.
413.78

c.
426.67

d.
698,009

e. None of these
are correct.

12. Which statement
below is the most meaningful interpretation of the
slope of the least-squares regression line?

a. The emotional
exhaustion index is estimated to decrease by 29.497 units for
every 1% increase in concentration.

b. The emotional
exhaustion index is estimated to increase by 8.865 units for
every 1% increase in concentration.

c. The percent
concentration is estimated to increase by 8.865 units for every
1 unit increase in emotional exhaustion.

d. The
least-squares slope, 8.865, is the smallest slope that can be
estimated using these data.

13. Which statement
below is the most meaningful interpretation of the
y-intercept of the median-median line?

a. The emotional
exhaustion index is -148.833 when concentration is
0%.

b. The emotional
exhaustion index increases by 148.833 units when concentration
is increased from 0% to 1%.

c. The
median-median line y-intercept has no meaningful
interpretation, because 0% concentration is outside the range
of the data.

d. The
median-median line cuts through the x-axis at
-148.833.

14. Which statement
below is the most meaningful interpretation of the sum
of the squared residuals for the least-squares regression
line?

a. No other
linear model will produce a larger sum of squared
residuals.

b. The large
value of the sum of the squared residuals indicates that a
straight-line model is of no use for predicting emotional
exhaustion (y).

c. No other
straight-line model fit to these data will produce a smaller
sum of the squared residuals.

15. A
box-and-whiskers plot is a visual representation best suited for
_?_ data.

a.
quantitative

b.
qualitative

c.
loose

d.
basketball

16. Among the
following statistics, which one is likely being used to help make
the following claim:

"Based on the sample, we are 95%
sure that the average speed of all drivers on this highway is
between 63 and 69 miles per hour"?

a. 5-number
summary

b.
mode

c.
median

d. standard
deviation

17. Which
of the following orders correctly represents the measures
of central tendency for the distribution shown
here?

This visual
representation shows test scores of 24 students in a statistics
course.

18. If m
students scored in the range shown and n students scored in
the range shown, which statement is most correct?

a. n >
m

b. n =
m

c. m =
15

d. n =
21

The following
situation is used for problems 19 and 20.

The distribution
of times that it takes to drive from Illinois Wesleyan
University to College Hills Mall at 5:00 pm on a weekday is
mound shaped (normal) with a mean of 18 minutes and a standard
deviation of 5 minutes.

19. Driving times
ranging from 13 minutes to 23 minutes represent approximately what
portion of all the driving times?

a.
5%

b.
13.5%

c.
27%

d.
34%

e.
68%

f.
95%

20. Determine a
driving time that will be exceeded by approximately 2.5% of all
drivers making the trip from IWU to College Hills Mall.

a. 8
minutes

b. 13
minutes

c. 18
minutes

d. 23
minutes

e. 28
minutes

f. 33
minutes

Part II: Open Response

Complete each question and write your response in the space
provided. Please include descriptive comments as necessary.

21. Here are the
results of the long jump and 50-meter dash for six middle-school
students.

Andy

Becky

Carl

Dan

Edna

Fran

x: jump length (ft)

y: dash time (sec)

15

6

12

8

17

6

9

10

11

10

14

8

a. On the grid
provided above, create a scatter plot for these data. Represent
jump length on the horizontal axis (x) and dash time on the
vertical axis (y).

b. Suppose that we
want to create a median-median line for these data. Begin
that process by finding the three median-median points used to
help determine the equation of the line. DO NOT go beyond this
step! You may show the ordered pairs on the scatter plot, but
also list them here.

c. When we complete
the process of determining the median-median line of best fit, the
equation is ,
where x represents a student's jump length and y
represents a student's dash time.

i) Interpret the
value
as it relates to these data and the median-median line.

ii) Interpret the
value
as it relates to these data and the median-median
line.

iii) Use the
median-median line to predict the dash time for a student who
jumped 10 feet.

b. Use your
calculator to generate the median-median line and the least
squares linear regression line for these data. Write each equation
in the form d = ma + b, where d is the diameter and
a is the tree age.

c. With respect to
the least-squares linear regression line, calculate the sum of the
squared residual values for the first five data values in
the table, that is, for the ordered pairs with ages 4, 5, 8, 8,
and 8. Show your calculations here.

23. A 1990s labor
dispute between the Major League Baseball Players' Association and
the team owners changed drastically the face of professional
baseball. During a recent spring, replacement players
populated the training grounds of the major league
teams.

Suppose we know that
the distribution of the ages, in years, of all replacement players
in spring training that season was mound shaped and symmetric
(normal).

a. If the mean age
of the replacement players was 20.4 years, and if 95% of the
replacement players ranged from 18.6 to 22.2 years old, determine
the standard deviation for the distribution. Show your
calculations.

b. Suppose, instead,
that the mean age of the replacement players was 21.1 years and
the distribution of ages had a standard deviation of 1.1 years.
Was it unlikely that a team has a replacement player who
would turned 24 years old during that training camp?
Explain.